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solveSystem -- solutions to a system of equalities

Description

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(x+3*y^2-2*z, x^2-2*y-z, 3*x-4*y+5*z^2)

              2            2             2
o2 = ideal (3y  + x - 2z, x  - 2y - z, 5z  + 3x - 4y)

o2 : Ideal of R
i3 : M = solveSystem(I)
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)
-- eigenvectors not matching, attempting computations of Jordan forms
-- multiplicities not computed due to
-- numerical errors in computing intersections of subspaces

o3 = Tally{{0, 0, 0} => 1}

o3 : Tally

Caveat

the procedure involves computation over inexact fields. If numerical errors occur, then the multiplicities of the solutions may be not reliable.

See also

Ways to use solveSystem:

  • solveSystem(Ideal)

For the programmer

The object solveSystem is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/NumericSolutions.m2:770:0.